In his seminal 1948 work [1]}, Shannon introduced the entropy power inequality (Shannon EPI) to show that “Gaussian is the worst additive noise”. Extensive research had been conducted to explore and generalize Shannon EPI [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. Besides its applications in various channel and source coding problems, Shannon EPI can be even used to prove the uncertainty principle and several other fundamental results in mathematical physics [5]}. Shannon EPI is far more than a common inequality in engineering but a profound characterization of Gaussian distribution in the language of entropy.
Costa [9]} in 1985 showed that \(\exp (2h(Y_t))\)  is concave, where the signs of the first and second derivatives of \(h(Y_t)\)  were obtained.
